Function Behavior and Graph Analysis

The video tutorial covers linear functions, focusing on increasing and decreasing functions. It explains how the graph of a function can describe relationships between quantities, highlighting the constant rate of change in linear functions. The lesson includes an exit card exercise analyzing graph intervals to identify increasing and decreasing functions. A real-world scenario involving a Ferris wheel is used to illustrate these concepts, showing how functions can increase, decrease, or remain constant over time.

What is a key characteristic of a linear function?

• It has a constant rate of change.

• It has a variable rate of change.

• It always decreases.

• It always increases.

What is the rate of change for a non-linear function?

• Always positive

• Variable

• Always negative

• Constant

How can you identify an increasing function from its graph?

• The graph has a negative slope.

• The graph is a vertical line.

• The graph has a positive slope.

• The graph is a horizontal line.

What does a decreasing function's graph look like?

• It has a positive rate of change.

• It is a vertical line.

• It has a negative rate of change.

• It is a flat line.

What is the significance of the graph's slope in determining function behavior?

• It indicates the function's speed.

• It shows the function's direction of change.

• It affects the function's length.

• It determines the function's color.

Can a function both increase and decrease over different intervals?

• Yes, it can.

• Only if it is a linear function.

• No, it cannot.

• Only if it is a non-linear function.

During which interval is the Ferris wheel's function increasing?

• 44 to 48 seconds

• 52 to 56 seconds

• 40 to 44 seconds

• 64 to 66 seconds

What happens during the interval from 60 to 64 seconds on the Ferris wheel?

• The Ferris wheel is stationary.

• The Ferris wheel is accelerating.

• The Ferris wheel is moving downwards.

• The Ferris wheel is moving upwards.

Which interval shows the Ferris wheel's function decreasing?

• 40 to 44 seconds

• 52 to 56 seconds

• 56 to 60 seconds

• 72 to 76 seconds

How many complete revolutions does the Ferris wheel make in the 40-second interval?

• Two revolutions

• Five revolutions

• Three revolutions

• Four revolutions